When do wireless network signals appear Poisson?

TL;DR

This paper investigates when the distribution of wireless signal strengths can be approximated by Poisson processes, providing theoretical bounds and conditions under which this approximation is valid for various network models.

Contribution

It establishes conditions and bounds for approximating the point process of wireless signals by Poisson or Cox processes, supporting simplified modeling of transmitter locations.

Findings

Signal strength point processes can be approximated by Poisson or Cox processes under general conditions.

Bounds on total variation distance quantify the approximation accuracy.

Results apply to common models with various transmitter placements and propagation effects.

Abstract

We consider the point process of signal strengths from transmitters in a wireless network observed from a fixed position under models with general signal path loss and random propagation effects. We show via coupling arguments that under general conditions this point process of signal strengths can be well-approximated by an inhomogeneous Poisson or a Cox point processes on the positive real line. We also provide some bounds on the total variation distance between the laws of these point processes and both Poisson and Cox point processes. Under appropriate conditions, these results support the use of a spatial Poisson point process for the underlying positioning of transmitters in models of wireless networks, even if in reality the positioning does not appear Poisson. We apply the results to a number of models with popular choices for positioning of transmitters, path loss functions, and distributions of propagation effects.